Torsion Formula
Torsion Formula - Related Videos
01:16
Torsion of Noncircular Members
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2024
Circular shafts undergoing torsional stress maintain their cross-sectional integrity due to their axisymmetric nature. This symmetry ensures an even distribution of stress, allowing the shaft to withstand torsion without distorting. In contrast, square bars, lacking this axial symmetry, experience significant distortion across their cross-sections when subjected to torsion, with the exception of along their diagonals and at lines connecting midpoints. A detailed examination of a cubic element...
01:09
Torsional Pendulum
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2025
A torsional pendulum involves the oscillation of a rigid body in which the restoring force is provided by the torsion in the string from which the rigid body is suspended. Ideally, the string should be massless; practically, its mass is much smaller than the rigid body's mass and is neglected. As long as the rigid body's angular displacement is small, its oscillation can be modeled as a linear angular oscillation. The amplitude of the oscillation is an angle. The role of mass is played by the...
02:52
Chemical Formulas
0 Views •
2020
A chemical formula presents information about the proportions of atoms constituting a particular chemical compound or molecule, mainly using symbols of elements and numbers. At times other symbols, such as dashes, parentheses, brackets, commas, plus, and minus signs, are also used. A chemical formula can be one of three types – molecular, empirical, and structural. Molecular Formula The molecular formula represents a molecule or a chemical compound using chemical symbols (to indicate the...
03:34
Ionic Compounds: Formulas and Nomenclature
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2020
An element composed of atoms that readily lose electrons (a metal) can react with an element composed of atoms that readily gain electrons (a nonmetal) to produce ions through complete electron transfer. The compound formed by this transfer is stabilized by the electrostatic attractions (ionic bonds) between the oppositely charged ions. Moving from the far right to the left on the periodic table, nonmetal elements often gain electrons to form anions with the same number of electrons as an atom...
01:20
Bending and Torsional Moments
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2025
Bending and torsional moments are two fundamental concepts in structural engineering. They play an important role in understanding the behavior of materials and structures under different loading conditions. The reaction developed in a structural element when subjected to an external force causes the element to bend. When a structural element bends upwards, it creates compressive normal forces on the top and tensile normal forces on the bottom, resulting in a couple that determines the bending...
FAQs
In τ = Tr/J, shear stress increases with radial distance r when torque T and polar moment of inertia J remain fixed. Material farther from the shaft center therefore experiences greater shear stress than material near the center. This relationship helps engineers identify the critical location for strength checks and evaluate how a member responds across its cross-section.
The polar moment of inertia J appears in both torsion relationships and represents the member’s geometric contribution to resisting twisting. A larger J reduces calculated shear stress and angle of twist for the same loading and length. The shear modulus G appears in θ = TL/GJ, linking material stiffness specifically to deformation rather than directly to the stress calculation.
The stated relationships apply to a circular member in elastic torsion, so the material must remain within the range where the equations appropriately describe its response. Engineers compare calculated shear stress with allowable stress limits and calculated twist with serviceability limits. These checks address both structural strength and whether deformation remains acceptable during operation.
A typical evaluation identifies the applied torque T, member dimensions needed for the polar moment of inertia J, the relevant radial location r, and the shaft length L. Engineers then calculate shear stress with τ = Tr/J and angle of twist with θ = TL/GJ. The results are compared with allowable stress and serviceability requirements before accepting the design.
For a proposed circular component, engineers use the stress relationship to determine whether its geometry can withstand the applied twisting moment and use the deformation relationship to check stiffness over the required length. Adjusting the member geometry changes J, while material selection changes G. Together, these calculations support sizing decisions for drive shafts and other power-transmission components.
A torsional analysis provides two complementary outcomes: the shear stress distribution associated with the applied torque and the member’s total angular deformation over its length. The first supports strength assessment, while the second supports stiffness and serviceability assessment. Considering both outcomes helps engineers predict operational behavior and determine whether a design remains within its intended limits.